Question

a school hires an artist to create a mural. the artist draws a model of the mural on a coordinate grid. each unit on the grid represents one foot. the school pays the artist $20 for each square foot of the mural. how much does the school pay the artist?

Explanation:

Step1: Find the length and width

The left - most x - coordinate of the mural is \(x = 2\) and the right - most x - coordinate is \(x=10\). So the length \(l=10 - 2=8\) feet.
The bottom - most y - coordinate is \(y = 1\) and the top - most y - coordinate is \(y = 7\). So the width \(w=7 - 1 = 6\) feet.

Step2: Calculate the area of the mural

The area of a rectangle (the mural is a rectangle) is given by the formula \(A=l\times w\). Substituting \(l = 8\) and \(w=6\), we get \(A=8\times6 = 48\) square feet.

Step3: Calculate the total payment

The school pays \(\$20\) per square foot. So the total payment \(P=20\times A\). Substituting \(A = 48\), we get \(P = 20\times48=960\).

Answer:

The school pays the artist \(\$960\).